Maths question involving coal reserves?

Question

If SA's coal reserves are estimated to be 45 000 million tons and SA produces on average 250 million tons of coal per year. If production increases at the rate of 6% per year how long will the reserves last?

Answer 1

Production increases at the rate of 1.06 per year.

For n years, that is (1.06)^n

see if we  can find an equation (millions of tons)

year 1: 250

year 2: 250(1.06)

year 3: 250(1.06)²

year 4: 250(1.06)³

Sum these up and set equal to 45000

45000 = 250 + 250(1.06) + 250(1.06)² +...+ 250(1.06)^(n-1)

4500 = 250 ((1.06) +(1.06)² +...+(1.06)^(n-1))

58 = (1.06) +(1.06)² +...+(1.06)^(n-1)

solve for n

here I get stuck...

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Answer 2

To 2 s.f: 89 years, as

250 million x (1.06) to the power 89 = 450 000